Establish the identity tan(2π−θ)=−tanθ. Which of the following four statements establishes the identity? A. tan(2π−θ)=1−tan2πtanθtan2π−tanθ=1−0⋅tanθ0−tanθ=−tanθ B. tan(2π−θ)=1−tan2πtanθtan2π+tanθ=1−1⋅tanθ1−tanθ=−tanθ c. tan(2π−θ)=1+tan2πtanθtan2π+tanθ=1+(−1)⋅tanθ1+tanθ=−tanθ D. tan(2π−θ)=1+tan2πtanθtan2π−tanθ=1+0⋅tanθ0−tanθ=−tanθ

Resuelto Establish the identity tan(2π−θ)=−tanθ. Which of the

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Pregunta: Establish the identity tan(2π−θ)=−tanθ. Which of the following four statements establishes the identity? A. tan(2π−θ)=1−tan2πtanθtan2π−tanθ=1−0⋅tanθ0−tanθ=−tanθ B. tan(2π−θ)=1−tan2πtanθtan2π+tanθ=1−1⋅tanθ1−tanθ=−tanθ c. tan(2π−θ)=1+tan2πtanθtan2π+tanθ=1+(−1)⋅tanθ1+tanθ=−tanθ D. tan(2π−θ)=1+tan2πtanθtan2π−tanθ=1+0⋅tanθ0−tanθ=−tanθ

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Paso 1
Establish the identity $\tan (2 π - θ) = - \tan θ$
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Texto de la transcripción de la imagen:

Establish the identity

tan (2 π - θ) = - tan θ

. Which of the following four statements establishes the identity? A.

tan (2 π - θ) = \frac{t a n 2 π - t a n θ}{1 - t a n 2 π t a n θ} = \frac{0 - t a n θ}{1 - 0 \cdot t a n θ} = - tan θ

tan (2 π - θ) = \frac{t a n 2 π + t a n θ}{1 - t a n 2 π t a n θ} = \frac{1 - t a n θ}{1 - 1 \cdot t a n θ} = - tan θ

tan (2 π - θ) = \frac{t a n 2 π + t a n θ}{1 + t a n 2 π t a n θ} = \frac{1 + t a n θ}{1 + ( - 1 ) \cdot t a n θ} = - tan θ

tan (2 π - θ) = \frac{t a n 2 π - t a n θ}{1 + t a n 2 π t a n θ} = \frac{0 - t a n θ}{1 + 0 \cdot t a n θ} = - tan θ